Introduction“Thediscoveryofcosmic-raycarbonhasanumberofinterestingimplications...particularlythedeterminationofagesofvariouscarbonaceous materials in the range of 1,000-30,000 years.”ThesearethewordswithwhichWillardF.Libbyandhiscoworkersconcluded their report on the first successful detection of 14C in biogenic material (Anderson et al., 1947). It was quite anunderstatement. Libby’s pioneeringworkon thedevelopmentof the radiocarbondatingmethodwonhim theNobel Prize inChemistry in1960,andasoneofhisnomineesaptlyobserved:“Seldomhasasinglediscoveryinchemistryhadsuchanimpactonthethinkingofsomanyfieldsofhumanendeavor.Seldomhasasinglediscoverygeneratedsuchwidepublic interest."(Taylor,1985).

Radiocarbondatinghascomealongwaysincethen.Itsphysicaland chemical principles are better understood, high-techinstrumentationhasimproveditsrangeandsensitivity,andthereare currently more than 130 active radiocarbon laboratoriesaroundtheworld.Theamountofliteratureonthesubjectisvastandwhatfollowsisjustanoverviewoftheessentials.Thedetailsmay be found in any of the books listed among the references at theendofthisarticle.Andso...

Basic PrinciplesCarbon-14 (14C) is a cosmogenic* radioactive isotope of carbonthat is produced at a more-or-less constant rate in Earth’s upper atmosphere by the reaction of neutrons generated by high-energy cosmic rays with nitrogen-14 (14N):†

14N + n(in) 14C + p(out)

wherenisaneutronandpisaproton.Carbon-14decaysbackto14Nbyemissionofaβ-particle(electron)withahalf-life(T½) of 5,730±40years:

14C 14N+β-(out)

About 1 part per trillion (1012) of Earth’s natural carbon is 14C.Therest,effectively100%,ismadeupofanapproximately99:1mixture of the stable isotopes carbon-12 (12C) and carbon-13 (13C) (fig.1).

Once formed, 14C is rapidly oxidized to carbon dioxide (14CO2), whichdiffuses throughout Earth’s atmosphere, dissolves in theoceans, and is taken up by green plants during photosynthesis andbyanimalsviathefoodchain(fig.2).Throughouttheirlivesplants and animals exchange carbon with their surroundings

Background: photo by Thomas Bresson used under Wikimedia Commons license CC BY 3.0

Lorraine A. Manz

Figure 1. Carbonnuclides.Anuclideisanatomicspeciescharacterizedby the number of protons (red spheres) and neutrons (gray spheres) in its nucleus.Nuclidesthathavethesamenumberofprotons(i.e.thesameatomicnumber,Z)butdifferentnumbersofneutronsarecalledisotopes.Carbon(Z=6)hasthreenaturallyoccurringisotopes.Althoughthetermsnuclide and isotope are commonly used interchangeably, they are not synonymous.

* Producedbycosmicrays.† Minor amounts are also derived from 15N, 16O, and 17O.

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andtherebymaintainaconstantconcentrationof14C.Provideditsproductionratedoesn’tchange, thiswillbeequal tothe 14C concentrationinatmosphericCO2.Whenlivingthingsdiecarbonexchange, and thus 14Creplacement,ceases.Deathhasnoeffecton radionuclides, however, so the 14C in the organisms’ remains continuestodecayandsteadilydepleteswithtime.

Like all radioisotopes, 14Cdecays exponentially at a rate that isproportionaltothenumberofradiocarbonatomsinthesample(fig.3). IfN0 is the number of 14Catomsattimet=0 (timeofdeath)andNisthenumberremainingaftertimet,thisprocesscanbedefinedbytheequation

ln(N0/N)=λt

inwhichλisaconstantequalto0.693/T½ and ln denotes a natural logarithm.Rearrangingthisequationandsubstitutingforλgives

t = (T½/0.693)ln(N0/N) (1)

So in principal, assuming that the level of atmospheric 14CO2

remainsconstantovertime,andalllivingthingscontainthesamerelative proportions of carbon isotopes as atmospheric CO2, N0

andNarebothmeasurablequantities. Since thehalf-lifeof 14C isalsoknown,theage(timeelapsedsincedeath)ofasampleofonce-livingmattercanbedeterminedbysolvingequation(1)fort.

Measuring RadiocarbonThere are two ways of measuring 14C(Aitken,2014).Theconventional method, also known as “beta-counting,”measures 14Cindirectlyfromitsrateofdecaybydetectingthe number of 14Cdecayevents(βparticleemissions)per

unit time per unit mass of sample. Conventional radiocarbondating techniques include gas proportional counting and liquidscintillationcounting(LSC).

Accelerator mass spectrometry (AMS) counts actual carbon atoms andmeasurestherelativeproportionsofeachofitsisotopes.Itisamuchmoreefficient(andexpensive)methodofdetecting14C than counting decay rates, but AMS’s greatest advantage overconventionaldatingmethodsisthatitssamplesizerequirementsare about 1,000 times smaller (milligrams vs grams). On theotherhand,conventionalbeta-countingisabletoachievehigherlevels of precision and lower background interference than AMS provided the sample is uncontaminated and sufficiently large.Becauseofthis,beta-countingtendstobethemethodofchoiceformeasuringradiocarboncalibrationcurves.

Radioisotopes are customarily measured against an internal standard, typically a stable isotope of the same element.Carbon-14isstandardizedto12Candexpressedastheratio14C/12C

Figure 3. Radioisotopes decay exponentially, which meansthatthepercentageofparentatomsdecayingperunitoftimeis constant. The half-life (T½) of a radioisotope is the time ittakesfor50%oftheatomstodecay;soifthereareN0 atoms at timet=0,therewillbeN0/2remainingafterthefirsthalf-life,N0/4afterthesecond,N0/8afterthethird,andsoon. Bythetimeeighthalf-liveshavepassed,99.6%oftheradioisotopehasdecayed. Carbon-14 reaches itsdetectable limit at thispoint,whent≈40,000years.

Figure 2. Thissimplifiedillustrationoftheglobalcarboncycleshowstheprincipalcarbonreservoirswiththeirrelativesizesexpressedaspercentages.Theamountofcarbonstoredinfossilfuelsandcarbonaterocks(geologiccarbon)isunknown.Because it is so old, most geologic carbon is devoid of 14C and is referred to as “dead”.

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so that N0 and N become (14C/12C)0 and (14C/12C)respectivelyandequation(1)canberewrittenas

t = (T½/0.693)ln(14C/12C )0 (2) (14C/12C)

Inordertocomparedatesfromotherlaboratories,radiocarbonages are calculated by comparing a sample’s measured 14C/12C ratiowiththatofauniversallyrecognizedstandard.AnumberoftheseexistbuttheprincipalradiocarbonstandardistheNationalInstitute of Standards and Technology’s (N.I.S.T.) Oxalic Acid 1(fig.4). Backgroundradiation ismeasuredusingblanksamples– typically coal, limestone or some other geologic material that containsonly“dead”carboni.e.,no14C – and the value obtained subtractedfromthesample’sradiocarbonmeasurement.

Dateable MaterialsTherelativelyshorthalf-lifeof14Cmeansthatradiocarbondatingcannot be applied to materials more than about 40,000 years old‡(fig.3).However,provideditmeetsthisrequirement,almostany organic material can be dated, which is why the method has revolutionized archaeology more than any other science.Radiocarbondatinghas alsoproven tobe immenselyuseful toQuaternary geologists. Besidesman-madeproducts like paperand fabric, many natural carbonaceous materials are capable of providing meaningful radiocarbon ages. These include wood,charcoal, peat and other organic-rich sediments, twigs, seeds, pollen, pine cones and needles, animal bones, shells, and even water(fig.5).

Calibrating and Correcting 14C AgesThere is more to calculating radiocarbon ages than simplypluggingnumbersintoequation(2).Althoughearlyradiocarbondates appeared to support the assumption that the level ofatmospheric 14CO2remainsconstantovertime(Libbyetal.,1949),as the technique evolved it soon became clear that this was not so.RadiocarbonagesareaffectedbyvariationsinthestrengthofEarth’smagneticfieldandsolaractivity–bothofwhichaffectthecosmicrayfluxandhencetherateof14Cproduction.Moreover,the large-scale burning of fossil fuels, which began during the industrial revolution; andmid-twentieth century above-groundnucleartestshavecontaminatedtheatmospherewithsignificant

Figure 4. Oxalic acid

Figure 5. Materials that can be radiocarbon dated include (clockwise from top) bone, peat and other organic-rich sediments, plant material such as seeds or pollen, groundwater, and woodorcharcoal.

Peat: photo by Jeff Delonge used under Wikimedia Commons license CC BY-SA 3.0. Tree stump: photo by Selby May used under Wikimedia Commons license CC BY 3.0. Water droplet: photo by Michael Melgar used under Wikimedia Commons license CC BY-SA 3.0. Picea seeds: Steve Hurst@USDA-NRCS PLANT

‡ Opinionsonthemaximumdetectionlimitofradiocarbondatingvaryfromabout40,000to75,000years. Itallboilsdowntothenatureofthe

sample,methodology,andinstrumentsensitivity.Inconventionalradiocarbondatingthemainlimitingfactorisbackground,whichsetsthemaximumageatabout40,000years.AMSmeasurementsarelimitedbyfactorsassociatedwiththeinstrumentitselfandanincreaseinthesignificanceofpossiblesamplecontaminationduetosmallersamplesizes.Isotopicenrichmentofsamplescanalsoextendagemeasurements.Datinglimitsvaryfromonelaboratorytoanotherandareusuallyspecifiedonreports.

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§ The PDB Marine Carbonate Standard was obtained from a Cretaceous-age marine fossil, Belemnitella americana,fromthePeeDeeFormationinSouthCarolina.ThePDBhasahigher13C/12Cratiothanalmostallotherformsofnaturallyoccurringcarbon.Forconvenience,itsδ13valueisdefinedaszero,whichmeansthattheδ13valuesofmostcarbonaceousmaterialsarenegative.

amounts of dead carbon and synthetic 14C (“bomb carbon”).Fortunately,itispossibletocorrectfortheseeffectsbecausetheyare recorded in the growth rings of trees and can therefore be dateddendrochronologically(seebox). Radiocarboncalibrationcurves based on the dendrochronology of long-lived trees such as the bristlecone pine and oak extend to about 11,000 BP (before present)(Friedrichetal.,2004).Othercalibrationmethodshavereliably pushed this limit to 26,000 years BP and beyond (Reimer etal.,2004,2009,2013).

The complicationsdonot end there. Correctionsmust alsobemade for natural variations in carbon isotope ratios caused byfractionation and in thedistributionof 14C between and within carbonreservoirs.

In radiocarbon dating, isotopic fractionation refers mainly tothepreferentialuptakeof lightercarbonbynaturalbiochemicalprocesses such as photosynthesis and bone growth, which can lead to significant depletionsof both 13C and 14C relative to 12C in plants and animals. Comparison of a sample’s 13C/12C ratio(knownasδ13)withanisotopicstandardsuchastheinternationalPee Dee Belemnite (PDB) standard carbonate§ or the equivalent Vienna-PDB standard (Coplen, 1994) quantifies the amountof fractionation that has occurred with respect to 13C. Thenecessarycorrectionisthenappliedbyassumingthattheeffectoffractionationon14C is double that on 13C.

Plants and animals that obtain carbon from sources other than the atmosphericreservoiroftenyieldanomalouslyhighradiocarbonages.Theradiocarbonagesoffishbonesandcharcoalknowntobethesameage,forexample,mightdifferbyasmuchasseveralhundredyears.Inthemarineenvironmentthisoffsetistheresultof the sheer vastness of the ocean and the extreme slowness andcomplexityoftheprocessesthatdrivethecirculationof itswaters. The distribution of dissolved 14C (as 14CO2) throughout the world’s oceans is consequently uneven both vertically andlaterally. Theneteffect isa reduction in the 14C content of the surface water, which gives it an apparent radiocarbon age of about 400 years. Knownas themarine reservoir effect, this isnot a problem likely to concern geologists in North Dakota, but its freshwatercounterpartis.

Lake and river waters are generally more homogeneous than ocean waters, so except in very rare cases the marine reservoir effect is absent. High apparent radiocarbon ages in freshwatersystems are caused primarily by the hard water effect – thepresence of dead carbon in the form of dissolved carbonates derived from calcite-rich rocks and sediments like limestone or marl. Old or dead carbon may also be introduced as CO2

released from sources that include humus, glacial meltwater, and volcanism. Or the water may become 14C-depleted owing toareductionintherateofCO2 exchange with the atmosphere caused by prolonged ice cover or unusually slow mixing of deep

and shallow lake water (Philippsen, 2013). Although the hardwatereffectislargelyafreshwaterphenomenon,itcanalsoaffectthe marine environment in estuaries and other places where thereisalargeinfluxofcarbonate-richfreshwater.

Unlike fractionation, reservoir effects are difficult to quantifybecause theyare influencedby somany variables. Formarinesamples a global marine reservoir correction is automaticallyapplied to radiocarbon ages (Reimer et al., 2009, 2013),whichmaybefurthermodifiedwithanadditionalcorrectiontoaccountforregionalvariationsinthemarinereservoireffect.CorrectionfactorsfordifferentoceanographicregionsaroundtheglobearestoredontheMarineReservoirCorrectionDatabaseatQueen’sUniversityinBelfast,NorthernIreland(ReimerandReimer,2001).These data are based on radiocarbon dates obtained from live specimensofknownagecollectedbeforenucleartestingbeganinthe1950s,andtheassumptionthatthecalculatedvaluesareconstant foragivenregion. Agediscrepanciesdue to thehardwatereffectrangefromafewdecadestoseveralcenturiesandareoftenunknown.Wherepossible,themagnitudeoftheeffectisdeterminedbyfollowingthemarineprotocolsi.e.,bycomparisonwith modern analogues from the same species and locality under assumedstableconditions(Bowman,1990).

It is generally assumed that materials considered suitable forradiocarbondatingareclosedsystemsinthesensethatallcarbonexchangewiththebiospherehasceased.Howeverthisisrarelytrue because direct exposure to other sources of carbon, which mayaffecttheir14Ccontent,isunavoidable.Thisisespeciallysoin the natural environment where dissolved inorganic carbonates, humic acids or modern plant fragments in soil, for example are common contaminants. Contamination can also happen if asampleisimproperlyhandledafterithasbeencollected.Contactwith modern carbon-containing products like paper, cloth, certainplasticsandeventhecollector’sbarehandscanall leadto inaccurate radiocarbondates (table1). Variousphysicalandchemical pretreatment methods are used to decontaminate samples prior to 14C analysis but they are not always successful (Bowman, 1990). The best option, especially where moderncontaminants are concerned, is to minimize or avoid themaltogetherbyadoptingcarefulsamplingandhandlingprocedures.

Table 1. Theeffect(inyears)ofmodernandold(dead)radiocarbon on actual 14Cage(Bowman,1990).

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Calculating and Reporting 14C AgesRadiocarbonagesarecalculatedusingequation2accordingtoarecommendedconventionthatincludesthefollowing:

• Use of the Libby half-life of 5,568 years (Libby, 1955), which is about 3% too low, rather than the more accurate (Cambridge) half-life of 5,730 years. Equation 2 thenbecomes

t = 8033 ln(14C/12C )0 (14C/12C)

The reason for using a half-life that is known to be incorrect is a historical one. The Cambridge half-life was officially recognized in 1962 (Godwin, 1962).Prior to that, radiocarbon dates were calculated using WillardLibby’sestimateof5,568years.Forthesakeofconsistency and to avoid errors when comparing pre- and post-Cambridge half-life radiocarbon ages, it was agreed thattheLibbyhalf-lifeshouldberetained.Radiocarboncalibrationcurvesautomaticallycorrectforthe3%errorinthecalculatedagethispracticeincurs.

• The assumption that the atmospheric 14C level is constant.

• Use of Oxalic Acid 1 or a related secondary standard as themodernradiocarbonstandard.

• Correction for sample isotopic fractionation bycomparisonwiththePDBstandard.

• Ages are expressed in years BP (before present) where 0 BPisdefinedasAD1950.Radiocarbonagescalculatedrelative to a fixed point in time are easy to comparebecause they are independent of the year they were measured. The choice of AD 1950 was made for noother reason than tohonor thepublicationof thefirstradiocarbondatesinDecember1949(Libbyetal.,1949).

Agescalculated in thiswayarecalledconventional radiocarbonages(CRA)(StuiverandPolach,1977;Stuiver,1980).ACRAistheage (in yearsBP) a samplewouldbehad theearly assumptionabout the constancy of atmospheric 14Clevelsbeencorrect.Itisusuallyreportedinaformatthatlookssomethinglikethis:

Beta-104380:8740±60BP

WhereBeta-104380 is thesamplereferencenumber,consistingofthedatinglaboratory’sidentifier,whichinthisexampleisBETA(= BetaAnalytic, Inc.) followedby a numeric code, 8740 is theradiocarbon age in years BP and 60 is the estimated standarderror (expressed as ± 1σ). Radiocarbon agesmay be roundedup according to convention (Stuiver and Polach, 1977) but notall laboratoriesdothis.(Note:Inradiocarbondating,BPalwaysmeans “years before 1950” but other datingmethods that usetheBPnotationmaydefine itdifferently. Thermoluminescencedating,forexample,definesBPasbeforeAD1980.Onoccasionswhen a distinction has to bemade, radiocarbon datesmay bereported in 14C yr BP i.e., carbon-14 or radiocarbon years BP.)CRAsareuncalibratedandonlycorrectforisotopicfractionation.Reservoir corrections, where necessary, are calculated andreportedseparately.

Materialswhosemeasuredradiocarbonisindistinguishablefrombackgroundi.e.,whoseageexceedsthemaximumdetectionlimitof the instrumentation cannotbe assigned afinite radiocarbonage. In such cases ages are usually reported as “greater thanthemeasurableupperage limit,”avaluethat isdependentnotonlyon thecountingmethodused (beta-orAMS)butalso thelaboratorydoing thework. Anagereportedas>40,000yr., forexample, means that the sample being dated is at least 40,000 yearsoldandanalternativedatingmethodmustbeconsidered.Attheotherendofthetimescale,aradiocarbonageoflessthan200yearsisreportedas“modern”or,ifitfallsafter1950,“greaterthanmodern.”

CalibrationofaCRAtranslatestheradiocarbonageintocalendaryears and corrects for the Libby half-life. Calibrated ages arealways expressed as a range in terms of cal AD, cal BC, or cal BP alongwiththeappropriateconfidencelevel–typicallyonesigma(σ) statistics (68%probability) and/or two sigma statistics (95%probability).(“Cal”inthiscontextmeanscalibrated,notcalendar.)ThecalibratedageattheonesigmaconfidenceleveloftheCRAdescribedabovecouldthereforebewrittenas:

calBC7950-7575(1σ)orcalBP9899–9524(1σ)

where cal BP = 1949 + cal BC (Stuiver and Pearson, 1993).(Similarly, cal BP = 1950 - cal AD, the reason for the switch from 1949to1950whenconvertingagesbeingthat there isnoyear0inAD/BCchronology.)BecausecalBCandcalADareequaltocalendar years BC and AD, calibrated radiocarbon dates are usually reportedusingoneorotherofthesenotationsratherthancalBP.Most CRAs are calibrated dendrochronologically using programs such as OxCal (Bronk, 2009), CALIB (Stuiver and Reimer, 1993;Stuiveretal.,2013),orWinCal25(vanderPlicht,1993).

Radiocarbon Dating in North Dakota The Catalog of NorthDakota RadiocarbonDates (Moran et al.,1973)isacompilationofarchaeologicalandgeologicradiocarbondatesfrommorethanthreedozensitesscatteredacrossthestate.Its approximately 90 entries represent all that were known totheauthorsatthetime,ofwhich justoverhalfaregeologicallysignificant(fig.6). Apartfromahandfulassociatedwithburiedglacialtills thatareclose toorbeyond theupperage limit, themajority of these dates record the timing, beginning about13,000yearsago,ofthefinalretreatoftheLaurentideicesheetfromNorthDakotaduringtheLateWisconsinanandtheregion’spostglacialhistory.

Intheforty-oddyearssincethecatalog’spublication,thenumberofNorthDakotaradiocarbondateshasalmosttripled.Inkeepingwith its authors’ primary intent, which was to “spare thoseworking on the Quaternary of this area the necessity of compiling individual lists,withattendantduplicationofeffort” thismainlypost-1973 data has been published in a revised and updated versionofthecatalog(seep.27).

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ReferencesAitken, M.J. 2014, Science-based Dating in Archaeology: New York,

Routledge,296p.Anderson,E.C.,Libby,W.F.,Weinhouse,S.,Reid,A.F.,Kirshenbaum,A.D.,

andGrosse,A.V.,1947,Radiocarbonfromcosmicradiation:Science,v.105,no.2735,p.576-577.

Bowman, S., 1990, Radiocarbon dating: Berkeley and Los Angeles,UniversityofCaliforniaPress,64p.

BronkR.C.,2009,Bayesiananalysisofradiocarbondates:Radiocarbon,v.51,no.1,p.337-360.

Coplen, T.B., 1994, Reporting of stable hydrogen, carbon, and oxygenisotopicabundances:PureandAppliedChemistry,v.66,p.273-276.

Friedrich,M.,Remmele, S., Kromer,B.,Hofmann, J., Spurk,M., Kaiser,K.F.,Orcel,C.,andKüppers,M.,2004,The12,460-yearHohenheimoak and pine tree-ring chronology from central Europe — A unique annual record for radiocarbon calibration and paleoenvironmentreconstructions:Radiocarbonv.46,no.3,p.1111-1122.

Godwin,H.,1962,Half-lifeofRadiocarbon:Nature,v.195,no.4845,p.984.Libby, W.F., 1955, Radiocarbon dating (2d ed.): Chicago, University of

ChicagoPress,175p.Libby,W.F., Anderson, E.C., and Arnold, J.R., 1949, Age determination

byradiocarboncontent–world-wideassayofnaturalradiocarbon:Science,v.109,p.227-228.

Moran,S.R.,Clayton,L.,Scott,M.W.,andBrophy,J.A.,1973,CatalogofNorthDakota radiocarbondates:NorthDakotaGeological SurveyMiscellaneousSeries53,51p.

Philippsen, B., 2013, The freshwater reservoir effect in radiocarbondating:HeritageScience,v.1,no.24,doi:10.1186/2050-7445-1-24.

Reimer, P.J., and Reimer, R.W., 2001, A marine reservoir correctiondatabaseandon-lineinterface:Radiocarbon,v.43,no.2a,p.461-463,http://radiocarbonpa.qub.ac.uk/marine/, (retrievedJune11,2014).

Reimer,P.J.,etal.,2004,IntCal04terrestrialradiocarbonagecalibration,26-0kaBP:Radiocarbon,v.46,no.3,p.1029-1058.

Reimer, P.J., et al., 2009, IntCal09 and Marine09 radiocarbon agecalibrationcurves,0-50,000yearscalBP:Radiocarbon,v.51,no.4,p.1111-1150.

Reimer, P.J., et al., 2013, IntCal13 and Marine13 radiocarbon agecalibrationcurves,0-50,000yearscalBP:Radiocarbon,v.55,no.4,p.1869–1887,doi;10.2458/azu_js_rc.55.16947,http://intcal.qub.ac.uk/intcal13/,(retrievedJune10,2014).

Stuiver,M.,1980,Workshopon14Cdatareporting:Radiocarbon,v.22,no.3,p.964-966.

Stuiver,M.,andPolach,H.A.,1977,Reportingof14Cdata:Radiocarbon,v.19,no.3,p.355-363.

Stuiver,M.,andPearson,G.W.,1993,High-precisionbidecadalcalibrationoftheradiocarbontimescale,AD1950-500BCand2500-6000BC:Radiocarbon,v.35,no.1,p.1-23.

Stuiver,M.,andReimer,P.J.,1993,Extended14CdatabaseandrevisedCALIB radiocarboncalibrationprogram:Radiocarbon,v.35,no.1,p.215-230.

Stuiver,M.,Reimer,P.J.,andReimer,R.W.,2013,CALIB7.0,http://calib.qub.ac.uk/calib/,(retrievedJune11,2014).

Taylor, R.E., 1985, The beginnings of radiocarbon dating in AmericanAntiquity-ahistoricalperspective:AmericanAntiquity,v.50,p.309-325.

vanderPlicht,J.,1993,TheGroningenradiocarboncalibrationprogram:Radiocarbon,v.35,no.1,p.231-237.

Figure 6. DistributionofgeologicallysignificantradiocarbondatesfromNorthDakota.BluedotsrepresentsamplecollectionsitesreportedintheCatalogofNorthDakotaRadiocarbonDates(Moranetal.,1973).Collectionsitesassociatedwithdatesnotincludedinthecatalog(publishedafter1973)areshownasyellowdots.

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